# Finite Sections of Periodic Schrödinger Operators

@article{Gabel2021FiniteSO, title={Finite Sections of Periodic Schr{\"o}dinger Operators}, author={Fabian Gabel and Dennis Gallaun and Julian Grossmann and Marko Lindner and Riko Ukena}, journal={ArXiv}, year={2021}, volume={abs/2110.09339} }

We study discrete Schrödinger operators H with periodic potentials as they are typically used to approximate aperiodic Schrödinger operators like the Fibonacci Hamiltonian. We prove an efficient test for applicability of the finite section method, a procedure that approximates H by growing finite square submatrices Hn. For integer-valued potentials, we show that the finite section method is applicable as soon as H is invertible. This statement remains true for {0, λ}-valued potentials with…

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